Control of a continuous fermentation with Saccharomyces cerevisiae is performed by manipulation of the feed flow rate using an ethanol measurement in the exit gas The process is controlled at the critical dilution rate with a low ethanol concentration of 40-50 mg/l. A standard PI controller is able to maintain the process satisfactory around the critical dilutio rate, but better performance is obtained with both an adaptive and a non-adaptive LQ controller. However, simulation results indicates that improved performance of the PI controller can be obtained using a simple approximate model to calculate the tuning parameters. The results show that linear, constant gain controllers give satisfactory performance when the process is maintained in a small operating region. Experiments with significant variations in process operation are necessary to demonstrate the advantages of adaptive control.